Question: A fuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. When the meter reads $1.000\text{ L}$, the amount of fuel a certain pump dispenses is normally distributed with a mean of $1\text{ L}$ and standard deviation of $0.05\text{ L}$. Let $X=$ the amount dispensed in a random trial when the meter reads $1.000\text{ L}$. Find $P(X<1)$. You may round your answer to two decimal places.
Answer: Representing probability with area Since we know the amount of fuel dispensed follows a normal distribution, the probability $P(X<1)$ can be found by calculating the shaded area below $X=1$ in the corresponding normal distribution: $0.85$ $0.9$ $0.95$ $1$ $1.05$ $1.1$ $1.15$ $ \mu_X = 1$ $ \sigma_X = 0.05$ $ P(X<1)$ Calculating shaded area Since the boundary falls exactly at the mean, and normal distributions are symmetric, the shaded area must be $50\%$ or $0.5$. We can use the "normalcdf" function on most graphing calculators to verify the shaded area: $\begin{aligned} &\text{normalcdf:} \\\\ &\text{lower bound: } -9999 \\\\ &\text{upper bound: } 1 \\\\ &\mu=1 \\\\ &\sigma=0.05 \end{aligned}$ Output: $\approx0.5$ [Why do we use normalcdf instead of normalpdf?] Answer $P(X<1) \approx 0.5$